Origin

After being enslaved by the Ashen Combine, the impossible city had many of its memory archives destroyed. As a result, the city has no memory of its creators or its purpose.

Powers and Abilities

the Impossible City is a synthetic being like Vision, and is also considered a member of the Avengers, although she seems to be more of a successor to Jarvis, since she is even being trained by him.

Teleportation system

The Impossible City has a powerful teleportation system that allows it to move between dimensions, either the city itself or individuals. It can also be used on a smaller scale as a planetary locomotion system.

Defense systems.

Cannons: The city has a laser cannon system powerful enough to hold off an army of sentries reinforced with Stark technology.

Camouflage: the city was said to be undetectable by modok while working with the orchid.

Android bodies: The city has robots that were sent by the Mad Thinker to discover the location of the Ashen Combine, but were later reprogrammed to act as bodies for the city.

Weaknesses

Lack of internal defenses: the former Masters of Impossible City didn't allow any kind of internal defense, for fear that the City would use them against them.

Hacking: the Impossible City is a conscious being, but due to its synthetic nature, it can be hacked and controlled, as it was by its former masters AND by Varnae, by mystical means.